# 4.3 Pricing with Market Power

Choosing a price is one of the most important decisions that a business makes for a particular product line. It is not always obvious whether you should increase or decrease the price in order to increase the company's profits. An increase in price may result in fewer units being sold. When changing the price, the tradeoff between the quantity and unit price must be examined very carefully.

What pricing and output decisions will maximise profits? A company's profit is defined as the difference between the total revenue of the firm (revenue=price x quantity) and the total cost of production. When the difference is negative, it is referred to as a loss.

A company can use demand and cost data to maximise its profits by applying the Marginal Revenue (MR) = Marginal Cost (MC) pricing rule whereby the profit maximising price, P, and quantity, Q, will be when MR=MC.

Of course, it is rare for a company to know its demand curve with any precision, but it can still use the MR=MC approach to make profit pricing and output decisions.

To find out how demand curve data, revenue and costs are used to calculate profits in general, and how that information is used to choose a price that will maximise profits, click the link here.

# Marginal Revenue (MR)

MR refers to the additional revenue earned by a firm from selling one additional unit of its output. It is the difference in total revenue when output is increased by one unit. Consider the demand and revenue information below.

 Price Per Unit (\$) Quantity Total Revenue (\$) MR (\$) 10 0 0 9 1 9 9 8 2 16 7 7 3 21 5 6 4 24 3 5 5 25 1 4 6 24 –1 3 7 21 –3 2 8 16 –5 1 9 9 –7

The above table shows that the MR from the first unit sold is \$9. This figure is the difference in total revenue when the firm expanded its output from zero units to one unit. MR measures the additional revenue the firm (a monopoly in this example) can earn by producing the first unit of output.

Similarly, the MR from selling the fifth unit of output is \$1. This is the difference in total revenue when the firm expands its output from four units to five units. This expansion in output changes total revenue from \$24 to \$25, giving a change of \$1. In other words, if the firm is producing four units, then it can generate additional revenue of \$1 by increasing production to five units. MR is shown graphically above. The graph and the table illustrate two facts about MR:

• MR can also be negative. For instance, the additional revenue generated by expanding production from five units to six units is –\$1. The firm will lose revenue by producing additional units of output.

• By comparing the first and the last columns of the table or looking at the graph, you can see that marginal revenue is always less than the price when the firm is producing two units of output or more. For instance, when the price is \$7 and the monopoly firm is selling three units, the MR from three units of output is only \$5.

Why is MR generally less than price? Suppose the firm is currently selling one unit of output. Since the price per unit is \$9, the firm is earning \$9 from selling this unit. Now suppose that the firm decides to produce and sell an additional unit of output. To sell the additional unit of output, the firm must reduce its price from \$9 to \$8. This is because consumers will buy additional units only if the price per unit is lower (the law of demand). Therefore, the firm will earn \$8 by selling the second unit. However, because the firm must sell all units for the same price, the first unit is now priced at \$8 instead of \$9.

Therefore, on the first unit, the firm will lose \$1 because of the price reduction. The net increase in the firm's revenue, the MR of the second unit, is only \$8 – \$1=\$7, which is less than the price of \$8. In general, MR is less than price because in selling an additional unit of output, a firm has to reduce prices on all earlier units because of the law of demand.

The above argument also shows why MR can be negative. Suppose the firm were producing five units of output at a price per unit of \$5. The firm would be earning total revenue of \$25 from selling these units. Now suppose that the firm decides to produce and sell an additional unit of output. In order to sell six units of output, the price per unit has to be reduced to \$4 to induce consumers to increase quantity demanded. The firm earns \$4 from selling the sixth unit at the price of \$4. However, the previous five units also have to be sold at \$4 instead of the earlier price of \$5. This implies that the firm now earns revenue of \$20 on these units instead of the \$25 earned earlier, and it means that the firm has incurred a loss of \$5 on the earlier units because of the price reduction. Therefore, the net increase in the firm's revenue, the MR from the sixth unit, is only \$4 – \$5=–\$1.

Click on the link here to see an example of calculating MR.

The information on MR is useful in making production decisions by identifying the range of output at which, irrespective of costs, it is never optimal to produce. For instance, you should never produce six, seven or eight units because marginal revenue is negative over this range. This means that producing these levels of output will lower your total revenue because producing greater output also means higher costs, and ultimately will lower profits (or increase losses).

# Marginal Cost (MC)

MC refers to the additional cost incurred by a firm in producing one more unit of output. It is the difference in total cost when output of the firm is increased by one unit. Consider the following table.

 Quantity Total Cost (\$) MC (\$) 0 1 1 5 4 2 6 1 3 8 2 4 11 3 5 16 5 6 22 6 7 30 8 8 40 10 9 52 12

In the above example, the MC of producing the third unit of output is \$2. It is the additional cost that the firm has to incur in order to expand production from two units to three units. # Determining Profit-Maximising Output

You can put the marginal revenue (MR) and MC (MC) together to determine the profit-maximising or loss-minimising output for the firm. First of all, given any output, Q, note the following marginal rules that specify whether a firm should or should not expand output from Q to Q+1:

• MR>MC at output Q+1: firm with market power should increase output from Q to Q+1

• If MR < MC at output Q+1: firm with market power should not increase output from Q to Q+1

MR is the additional revenue generated if the firm increases output by one unit from Q to Q+1. MC is the additional cost of producing this one unit of output. If MR>MC, then the additional revenue generated from the selling unit Q+1 is greater than the additional cost. Therefore, it is profitable for the firm to produce and sell this unit of output. If, on the other hand, MR < MC, then producing and selling this unit of output loses money for the firm; therefore, this unit of output should not be produced.

Click on the link here for an example of deciding whether or not to expand output.

To read about how the MR=MC rule applies to an airline, click the link here.

# Profit-Maximising Output Through Marginal Analysis

The MR=MC rule can be used to identify the profit-maximising output for a firm with market power. At the profit-maximising output Q, MR=MC. There is no incentive for a firm to reduce or increase output, because any such change will reduce the profits of the firm. If the firm reduces its output by one unit, the additional revenue generated from selling one more unit is equal to the additional cost of producing one more unit. The firm's profits are the same at both the profit-maximising Q and the lower output Q–1 and no additional profits are generated by reducing output. On the other hand, expanding output by one unit loses money for the firm since MR is less than MC.

The profit-maximising output for a monopoly firm is shown in the graph below. To the left of the profit-maximising output Q*, MR>MC; therefore, the firm should expand output. On the other hand, to the right of Q*, MR < MC; therefore, having reached the output level Q*, the firm should not expand output beyond Q*.

Consider the following data.

 Price per unit (\$) Quantity (units) MR (\$) MC (\$) Profits (\$) 10 0 –1 9 1 9 4 4 8 2 7 1 10 7 3 5 2 13 6 4 3 3 13 5 5 1 5 9 4 6 –1 6 2 3 7 –3 8 –9 2 8 –5 10 –24 1 9 –7 12 –43

The output choice of the firm can be identified by observing that

• MR=MC=\$3 when output is four units.

• MC is increasing. MR=\$1 < MC=\$5 when output is five units.

Therefore, the firm should produce four units of output and should charge a price of \$6 per unit. There is no other output level at which the firm earns higher profits.

Another example, which is easier to understand, is when a company has a constant MC. Click on the link here to work through an example where this is the case.

Click the link here to find out how profit is maximised with limited information.

# Solving for Price with the MR Curve

Many of the examples that describe marginal analysis look at the pricing and output decisions of firms with market power using discrete quantities of 1, 2, 3, etc. Moreover, they purposely look only at very small markets in which outputs vary over a limited range (from 0 to 9) as a way of seeing the operation of the MR=MC rule.

However, the MR=MC rule can be used much more generally. The MR=MC pricing rule can be used in markets in which quantities vary continuously. It can also be used in markets in which outputs are much greater than in the examples considered in the previous examples.

Click the link here to find out how to use MR=MC analysis in markets with linear demand curves of the kind you learned about in topic 3.3.

You may also be wondering how to use MR=MC analysis if there is incomplete information about a firm's demand curve. This case is discussed next. In the real world, firms have only a limited knowledge of their demand and marginal revenue curves. Therefore, it is difficult to apply the rule of equating MR with MC to determine the optimal level of production and the price per unit. Moreover, although linear demand curves are a mathematically convenient tool, demand curves will, in practice, take many different shapes, sometimes non-linear. However, if the firm knows its MC of production and the elasticity of demand (e), then it can use the following rule for setting its pricing policy: Click the link here to find out how this formula is mathematically derived.

To learn more about monopoly pricing and elasticity, view the following animation.

# Inverse Elasticity Pricing Rule

The inverse elasticity pricing (IEPR) rule is a central feature in price setting that pulls together two factors that affect the choice of price. One is the demand side, willingness to pay and the demand elasticity, and the other is the cost side.

The best pricing rule is a mixture of the two. And that's exactly what the IEPR does. It tells you that you should mark your price up over the MC by an amount that depends on the demand elasticity. So if demand is very elastic, you have a fairly small markup over cost, and the market won't bear a very high price. If the demand is very inelastic, then you mark it up over cost because the market will bear quite a high price.

## Implications of the IEPR rule

The IEPR rule can be used to determine the firm's price if the firm knows its MCs of production as well as what its elasticity should be at its profit-maximising production level, but lacks information on its demand curve and marginal revenue. It can also be applied to those situations in which the firm's MCs and elasticity of demand do not vary considerably over the range of output in which the optimal production level is located; the above rule helps the firm to approximately determine its optimal price.

This rule has other implications as well. First, if a product has highly elastic demand, then 1 ÷ e will be small and price will be close to MC. Therefore, when a product has many close substitutes, the gap between price and MC is small, and the firm's market power is low. On the other hand, if the product has highly inelastic demand, the gap between price and MC will be high; implying that market power is high.

As discussed in topic 4.2, the extreme case of a firm lacking market power is when it is a price-taker. For such a firm, demand is horizontal, or perfectly elastic (ie, elasticity of demand is equal to infinity). In this case, 1 ÷ e is very close to zero. Therefore, the pricing rule states that in this case P=MC. In other words, a price-taking firm will find it profitable to expand output to the point at which the MC of production is equal to the market price.

The rule also implies that a monopoly will never operate on the inelastic portion of the demand curve. Why is this the case? If demand is inelastic, –1 < e < 0, so that (1 ÷ e) < 0 and [1 + (1 ÷ e )] < 0. Because MC is always positive, the primary rule would imply that P=MC ÷ [1 + (1 ÷ e)] would be negative. Therefore, for price to be positive, [1 + (1 ÷ e)]>0 or e < 1 must be true or the firm must be operating on the elastic portion of its demand.

The rule also indicates how an increase in MC will influence the firm's price. In particular, it shows that every dollar increase in the firm's MC will increase price by a factor of 1 ÷ [1 + (1 ÷ e)]=e ÷ (1 + e). For instance, if the elasticity of demand is –3, then an increase in MC by \$10 will increase the price charged by the firm by \$15.

If different consumers have different elasticities, the pricing rule indicates how, for a given MC, the price charged will be different for different buyers. In particular, if e is relatively small, then the price charged will be relatively high. This explains why firms sometimes charge different prices for the same product, a phenomenon that is referred to as "price discrimination". For instance, telephone companies will generally charge businesses a higher price for phone calls than individuals. The MC of providing the phone service to a business and to an individual for private use is the same. However, businesses have a relatively inelastic demand for phone services and therefore have to pay a higher price.

Click the link here to find out how you can use the IEPR rule to determine the optimal price.

## What does the IEPR rule suggest for inelastic demand?

One implication of the IEPR is that monopolists will never operate in the inelastic portion of the demand curve. This is simple to see with linear demand: at any portion of the demand curve where demand is inelastic, the monopolist can raise revenues by increasing the price.

Click on the link here for a discussion of the impact on Canadian tobacco sellers from the US tobacco industry settlement. It illustrates the relationship between variable and fixed costs as well as demand-side substitution.

Click on this Discussion for details on your discussion activity.

To get a feel of how to work through a full pricing problem, click here for a guided practice.

# Topic Summary

• This topic demonstrated how to calculate a firm’s marginal revenue.

• A firm's MR and MC can be used to determine the output level that maximises profits.

• A firm’s profit-maximising price can be related to its price elasticity of demand and the IEPR derived.

You may now proceed to topic 4.4, "Pricing Strategies".